The generator matrix

 1  0  0  0  1  1  1  X  1 aX  1  1  X  1  1  0  1  1  1 aX  1  1 (a+1)X  1  X  1  1  0  1  1  1  1 aX  1  1  1  1  1  1  1  1  1
 0  1  0  0  X  1 X+1  1 (a+1)X  1 (a+1)X+1  0  1 X+1 aX+1  1 aX X+a+1 (a+1)X+a+1  1  X a+1  1  0  1 (a+1)X+a aX+a+1  1  a  X X+a (a+1)X aX  1 aX+a+1 aX+a+1 aX+a+1 (a+1)X+a+1  a a+1 (a+1)X+a (a+1)X+1
 0  0  1  0 (a+1)X+1  1 (a+1)X (a+1)X+1 aX+1  a aX (a+1)X+a aX+1 a+1  a a+1 (a+1)X+a+1  1 X+a+1  X (a+1)X+a (a+1)X+1 a+1  X (a+1)X+a+1 aX+a+1 (a+1)X+a (a+1)X aX+a+1 X+a aX+a  X  1 aX+1 a+1 X+a (a+1)X aX+1 aX+1 aX+a+1 (a+1)X (a+1)X+a
 0  0  0  1 a+1  X aX+a+1 aX+a+1  a aX (a+1)X+a aX (a+1)X+a (a+1)X  1 (a+1)X+1 aX+1 aX+a+1 (a+1)X+a+1  1 X+1  a (a+1)X+a+1 (a+1)X+1  0 (a+1)X+1  0 a+1 aX+a (a+1)X+a aX+1 aX+a+1 (a+1)X+a aX+1  X X+a+1 (a+1)X+a (a+1)X (a+1)X+a (a+1)X+1 aX+a+1  a

generates a code of length 42 over F4[X,sigma]/(X^2) who´s minimum homogenous weight is 113.

Homogenous weight enumerator: w(x)=1x^0+708x^113+1440x^114+528x^115+93x^116+2676x^117+3120x^118+1140x^119+153x^120+4584x^121+4992x^122+2112x^123+351x^124+6888x^125+7176x^126+2472x^127+99x^128+7476x^129+6888x^130+2352x^131+249x^132+4452x^133+3432x^134+516x^135+48x^136+864x^137+600x^138+96x^139+21x^140+6x^148+3x^152

The gray image is a linear code over GF(4) with n=168, k=8 and d=113.
This code was found by Heurico 1.16 in 87.7 seconds.